Summary: A cubic complex Ginzburg-Landau model is derived for the flow of a general fluid near a bifurcation point. Solutions are obtained for the natural convection flow of air in a differentially heated tall closed cavity under non-Boussinesq conditions. The model is used to analyse various types of instabilities. In particular, it is found that nonlinear fluid property variations with temperature lead to a convective instability of the flow when the temperature difference becomes sufficiently large. This is in contrast with classical results in the Boussinesq limit where the instability is found to be always absolute. The results obtained using the model for an infinitely tall cavity are in excellent agreement with those of direct numerical simulations for a cavity of aspect ratio 40.